There is known a dual clutch transmission where gear trains are provided to each of a portion between a first input shaft and an output system and a portion between a second input shaft and the output system, and one of the two input shafts is selectively connected to an internal combustion engine. Further, there is known a hybrid vehicle where such a dual clutch transmission is mounted, electric motors are connected to the input shafts respectively, and gear trains corresponding to first, third and fifth speed stages are provided between one of the input shafts and the output system while another gear trains corresponding to second, forth, and sixth speed stages being provided between the other one of the input shafts and the output system (see the patent literature 1). In addition, there are the patent literatures 2 and 3 as prior art literatures of the present invention.